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Function transformations 
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#1
Jan3014, 08:02 PM

P: 55

Hello all, I need some help to clear my doubts.
Why does a horizontal translation (f(x + c)) move to the left if c is positive? Can someone graphically explain what effect a stretch and compression (vertical and horizontal) has on the original parent function? Similar to the first question, why does f(ax) actually stretch by a factor of 1/a instead of a? Thanks, I might have more questions later. 


#2
Jan3114, 07:28 AM

P: 627

Is you graph y1=f(x) and y2=f(x+C) and then compare them, whatever "y1" you see at any "x1" will be seen to the left (assuming C>0) at x2="x1C" for y2 because y2 = f(x2+C) = f(x1C+C) = f(x1) = y1.
Similarly: f(Ax) will horizontally thin the graph by a factor of "A" (or stretch it by 1/A) Af(x) will vertically stretch the graph by a factor of "A". 


#3
Jan3114, 11:49 PM

P: 255

Take a look at this simple example, suppose ##f(x)=x##, a simple straight line through the origin. If ##x=0##, then ##f(x)=0## as well. But if you take ##f(x+a)##, the origin will be at ##a##. If you draw the line, the origin will move to the left because the origin is now in negative part of the xaxis.



#4
Feb114, 01:51 PM

Mentor
P: 21,397

Function transformations



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